Radio de estabilidad real de sistemas bidimensionales para perturbaciones lineales dependientes del tiempo.
Rayleigh principle for linear Hamiltonian systems without controllability∗
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Rayleigh principle for linear Hamiltonian systems without controllability∗
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Reducibility and point spectrum for linear quasi-periodic skew-products.
Reguläre Eigenwertprobleme mit Mehrpunkt-Integral-Randbedingungen.
Regularized trace of the Sturm-Liouville operator with irregular boundary conditions.
Regularized traces and conditions of smooth periodicity for the potential of Sturm-Liouville equation.
Relative boundedness and compactness theory for second-order differential operators.
Relatively bounded and compact perturbations of th order differential operators.
Remark on Sturm-Liouville functions
Remark to the problem of eigenvalues of Schrödinger equation
Remarks on nonlinear noncoercive problems with jumping nonlinearities
Remarks on semilinear problems with nonlinearities depending on the derivative.
Renormalization of exponential sums and matrix cocycles
In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics
Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space
We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
Résurgence de Voros et périodes des courbes hyperelliptiques
Le but de cet article est de formuler de façon géométrique l’idée maîtresse de Voros dans Ann. Inst. Henri Poincaré, Sect. A 39, 211-238 (1983) : les solutions de l’équation de Schrödinger stationnaire à une dimension, à potentiel polynomial, sont codées exactement dans le domaine complexe par leurs développements BKW (développements formels, divergents, en puissances de la constante de Planck), d’une façon entièrement lisible dans la géométrie des périodes de la forme (=variable de position,...
Riesz Bases of Solutions of Sturm-Liouville Equations.